You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $20 for the ace of clubs. 1. Create a probability model for the amount you win. 2. Find the expected amount you’ll win. 3. What would you be willing to pay to play this game?
> The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weight-in-motion scale. To see if the new device was accurate, they conducted a calibrati
> The Atlas Body Building Company (ABC) sells starter sets of barbells that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pounds. The weights average the specifi
> At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut. The shop owner believes that the number of cups he sells each day is Normally distributed with a mean of 320 cups and a standard deviation of 20 cups. He also beli
> The bicycle shop in Exercise 50 will be offering 2 specially priced children models at a sidewalk sale. The basic model will sell for $120 and the deluxe model for $150. Past experience indicates that sales of the basic model will have a mean of 5.4 bike
> A farmer has 100 lb of apples and 50 lb of potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0.5 dollars and a standard deviation of 0.2 dollars. Similarly, for a pound of potatoes, the mean price is
> Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take: The times
> In the 4—100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the follow
> You’re thinking about getting two dogs and a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described in Exercise 46 . 1. Define appropriate variables and express the total annua
> In Exercise 45 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounces. 1. Find the expected amount of cere
> The American Veterinary Association claims that the annual cost of medical care for dogs averages $100, with a standard deviation of $30, and for cats averages $120, with a standard deviation of $35. 1. What the expected difference in the cost of medical
> The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one
> For the roller coaster data in Exercise 49: 1. Explain why in looking for a variable that explains rank, you will be hoping for a negative correlation. 2. Do any of the provided variables provide a strong predictor for roller coaster rank?
> A casino knows that people play the slot machines in hopes of hitting the jackpot but that most of them lose their dollar. Suppose a certain machine pays out an average of $0.92, with a standard deviation of $120. 1. Why is the standard deviation so larg
> An insurance company estimates that it should make an annual profit of $150 on each homeowner policy written, with a standard deviation of $6000. 1. Why is the standard deviation so large? 2. If it writes only two of these policies, what are the mean and
> Organizers of a televised fundraiser know from past experience that most people donate small amounts ($10 $25), some donate larger amounts ($50 $100), and a few people make very generous donations of $250, $500, or more. Historically, pledges average abo
> A delivery company trucks occasionally get parking tickets, and based on past experience, the company plans that each truck will average 1.3 tickets a month, with a standard deviation of 0.7 tickets. 1. If they have 18 trucks, what are the mean and stand
> Find the mean and standard deviation of the number of red lights the commuter in Exercise 24 should expect to hit on her way to work during a 5-day work week.
> Find the mean and standard deviation of the number of repair calls the appliance shop in Exercise 23 should expect during an 8-hour day.
> A company selling vegetable seeds in packets of 20 estimates that the mean number of seeds that will actually grow is 18, with a standard deviation of 1.2 seeds. You buy 5 different seed packets. 1. How many bad (non-growing) seeds do you expect to get?
> A grocery supplier believes that in a dozen eggs, the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy 3 dozen eggs without checking them. 1. How many broken eggs do you expect to get? 2. What the standard deviation? 3. Wh
> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. 2Y+20 2. 3X 3. 0.25X+Y 4. X5Y 5. X1+X2+X3
> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. 0.8Y 2. 2X100 3. X+2Y 4. 3XY 5. Y1+Y2
> For the roller coaster data in Exercise 49: 1. Examine the relationship between Initial Drop and Speed. 2. Examine the relationship between Initial Drop and Height. 3. What conclusions can you safely draw about the initial drop of a roller coaster? Is In
> A random sample of 1000 patients was taken from a large medical center database. The six variables included are Sex (M/F), Age (years), Insurance coverage (yes/no), Number of children (010), Marital status (single, married, divorced, widowed), Number of
> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. X20 2. 0.5Y 3. X+Y 4. XY 5. Y1+Y2
> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. 3X 2. Y+6 3. X+Y 4. XY 5. X1+X2
> In a litter of seven kittens, three are female. You pick two kittens at random. 1. Create a probability model for the number of male kittens you get. 2. What the expected number of males? 3. What the standard deviation?
> In a group of 10 batteries, 3 are dead. You choose 2 batteries at random. 1. Create a probability model for the number of good batteries you get. 2. What the expected number of good ones you get? 3. What the standard deviation?
> Your company bids for two contracts. You believe the probability you get contract #1 is 0.8. If you get contract #1, the probability you also get contract #2 will be 0.2, and if you do not get #1, the probability you get #2 will be 0.3. 1. Are the two co
> You play two games against the same opponent. The probability you win the first game is 0.4. If you win the first game, the probability you also win the second is 0.2. If you lose the first game, the probability that you win the second is 0.3. 1. Are the
> An option to buy a stock is priced at $200. If the stock closes above 30 on May 15, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $200.
> Mary is deciding whether to book the cheaper flight home from college after her final exams, but she unsure when her last exam will be. She thinks there is only a 20% chance that the exam will be scheduled after the last day she can get a seat on the che
> An insurance policy costs $100 and will pay policyholders $10,000 if they suffer a major injury (resulting in hospitalization) or $3000 if they suffer a minor injury (resulting in lost time from work). The company estimates that each year 1 in every 2000
> A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While none had more than three of these defects, 7% had three, 11% two, and 21% one defect. Find the expected number of appearance d
> Since 1994, the Best Roller Coaster Poll (www.ushsho.com/bestrollercoasterpoll.htm) has been ranking the world best roller coasters. In 2013, Bizarro dropped to 4th after earning the top steel coaster rank for six straight years. Data on the top 14 steel
> A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below. 1. How many red lights should she expect to hit
> The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. 1. How many calls should the shop expect per hour? 2. What is the standard deviation?
> Find the standard deviation of your winnings throwing darts in Exercise 14 .
> Find the standard deviation of the number of children the couple in Exercise 13 may have.
> Find the standard deviation of the amount you might win rolling a die in Exercise 12 .
> Find the standard deviation of the amount you might win drawing a card in Exercise 11 .
> Find the standard deviations of the random variables in Exercise 10 .
> Find the standard deviations of the random variables in Exercise 9 .
> A man buys a racehorse for $20,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $100,000. If it wins one of the races, it will be worth $50,000. If it lose
> A small software company bids on two contracts and knows it can only get one of them. It anticipates a profit of $50,000 if it gets the larger contract and a profit of $20,000 on the smaller contract. The company estimates there a 30% chance it will get
> In a dataset of 1057 New York homes offered for sale, a histogram of the ages looks like this: We drew 1000 samples of 105 homes from this dataset and found the IQR and the range of each sample. Below are histograms of the 1000 IQRs and 1000 ranges. For
> A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $5 to play, and you’re willing to spend up to $20 trying to win. You estimate that you have about a 10% chance of hitting the balloon on any th
> A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.) 1. Create a probability model for the number of children they might h
> You roll a die. If it comes up a 6, you win $100. If not, you get to roll again. If you get a 6 the second time, you win $50. If not, you lose. 1. Create probability model for the amount you win. 2. Find the expected amount you’ll win. 3. What would you
> Find the expected value of each random variable:
> A certain company believes that 95% of its job applicants are trustworthy. The company gives everyone a polygraph test, asking, Have you ever stolen anything from your place of work? Naturally, all the applicants answer No, but the polygraph identifies
> Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There ha
> In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were (correctly) positive, while for people without HIV 98
> A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only
> Dan Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3% of the dishes he washes. (He, of course, will need
> Return to the data on roller coasters seen in Exercise 23. Here is the distribution of the lengths of the rides of 241 coasters. We drew samples of 60 coasters from the full set of 241. We then repeated this 1000 times. For each sample, we found the mean
> An airline offers discounted advance-purchase fares to customers who buy tickets more than 30 days before travel and charges regular fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage o
> Police often set up sobriety check points roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. If the officer does not suspect a problem, drivers are released to go on th
> Given the e-reader data presented in Exercise 52: 1. If a randomly selected U.S. adult has an e-reader, what is the probability that he or she hasn’t read an e-book in the past year? 2. Is it more or less likely that a randomly selected U.S. adult who do
> At the company described in Exercise 51, what percent of the absent employees are on the night shift?
> Pew Internet reported in January of 2014 that 32% of U.S. adults own at least one e-reader, and that 28% of U.S. adults read at least one e-book in the previous year (and thus, presumably, owned an e-reader). Overall, 76% of U.S. adults read at least one
> A company records indicate that on any given day about 1% of their day-shift employees and 2% of the night-shift employees will miss work. Sixty percent of the employees work the day shift. 1. Is absenteeism independent of shift worked? Explain. 2. What
> What percent of students who graduate from the college in Exercise 48 attended a public high school?
> Remember Leah (Exercise 47)? Suppose you pick her up at the Denver airport, and her luggage is not there. What is the probability that Leah first flight was delayed?
> A private college report contains these statistics: 70% of incoming freshmen attended public schools. 75% of public school students who enroll as freshmen eventually graduate. 90% of other freshmen eventually graduate. 1. Is there any evidence that a fre
> Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first fl
> Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2016 season. (Data in Attendance 2016) 1. Do winning teams generally enjoy greater attendance at their home games? Describe the associa
> A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Is country of origin independent of type of driver?
> A poll conducted by Gallup classified respondents by sex and political party, as shown in the table. Is party affiliation independent of the respondents sex? Explain.
> After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30. 1. What percent of the respondents were 30 or less and did not sno
> According to estimates from the federal government 2010 National Health Interview Survey, based on face-to-face interviews in 16,676 households, approximately 63.6% of U.S. adults have both a landline in their residence and a cell phone, 25.4% have only
> Given the table of probabilities from Exercise 24, are party affiliation and position on immigration independent? Explain.
> Given the table of probabilities from Exercise 23, are high blood pressure and high cholesterol independent? Explain.
> In Exercises 20 and 26, we looked at the birth orders and college choices of some Intro Stats students. For these students: 1. Are enrolling in Agriculture and Human Ecology disjoint? Explain. 2. Are enrolling in Agriculture and Human Ecology independent
> Early in 2010, Consumer Reports published the results of an extensive investigation of broiler chickens purchased from food stores in 23 states. Tests for bacteria in the meat showed that 62% of the chickens were contaminated with campylobacter, 14% with
> The local animal shelter in Exercise 22 reported that it currently has 24 dogs and 18 cats available for adoption; 8 of the dogs and 6 of the cats are male. Are the species and sex of the animals independent? Explain.
> If you draw a card at random from a well-shuffled deck, is getting an ace independent of the suit? Explain.
> American League baseball games are played under the designated hitter rule, meaning that pitchers, often weak hitters, do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendan
> According to Exercise 16, the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. 1. What the probability that someone who has traveled to Mexico has visited Canada too? 2. Are traveling to M
> A survey found that 73% of Americans have a home phone, 83% have a cell phone and 58% of people have both. 1. If a person has a home phone, what the probability that they have a cell phone also? 2. Are having a home phone and a cell phone independent eve
> Fifty-six percent of all American workers have a workplace retirement plan, 68% have health insurance, and 49% have both benefits. We select a worker at random. 1. What the probability he has neither employer-sponsored health insurance nor a retirement p
> A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a statistics course or a computer course. By the time they are juniors, 52% of the biology majors have
> The soccer team shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of e
> A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome. 1. The first two you choose are both good. 2. At least one of the fi
> You pick three cards at random from a deck. Find the probability of each event described below. 1. You get no aces. 2. You get all hearts. 3. The third card is your first red card. 4. You have at least one diamond.
> You are dealt a hand of three cards, one at a time. Find the probability of each of the following. 1. The first heart you get is the third card dealt. 2. Your cards are all red (that is, all diamonds or hearts). 3. You get no spades. 4. You have at least
> Twenty percent of cars that are inspected have faulty pollution control systems. The cost of repairing a pollution control system exceeds $100 about 40% of the time. When a driver takes her car in for inspection, what the probability that she will end up
> Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever also have sore throats. What the probability that a kid who goes to the doctor has a fever and a sore throat?
> In the previous exercise you analyzed the association between the amounts of fat and sodium in fast food hamburgers. What about fat and calories? Here are data for the same burgers: a) Analyze the association between fat content and calories using correl
> Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 20. 1. If we select a student at random, what the probability the person is an Arts and Sciences student who is a second child (or more)? 2.
> Look again at the table summarizing the Roper survey in Exercise 19. 1. a) If we select a respondent at random, what the probability we choose a person from the United States who has done post-graduate study? 2. Among the respondents who have done post-g
> The table shows the political affiliations of U.S. voters and their positions on supporting stronger immigration enforcement. 1. What the probability that 1. a randomly chosen voter favors stronger immigration enforcement? 2. a Republican favor
> The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table What the probability that 1. a man has both conditions? 2. a man has high blood pressure? 3. a man with high blood pressure has high chole
> In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random
> You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities: 1. The card is a heart, given that it is red. 2. The card is red, given that it is a heart. 3. The card is an ace, given that it is red. 4.
> A survey of students in a large Introductory Statistics class asked about their birth order (1=oldest or only child) and which college of the university they were enrolled in. Here are the data: Suppose we select a student at random from this class. What
> The marketing research organization GfK Roper conducts a yearly survey on consumer attitudes worldwide. They collect demographic information on the roughly 1500 respondents from each country that they survey. Here is a table showing the number of people
> Employment data at a large company reveal that 72% of the workers are married, that 44% are college graduates, and that half of the college grads are married. What the probability that a randomly chosen worker 1. is neither married nor a college graduate
> A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TVs, and 21% had both a TV and a refrigerator. What the probability that a randomly selected dorm room has 1. a TV but no refrigerator? 2. a TV or a refrigerator
> Fast food is often considered unhealthy because much of it is high in both fat and sodium. But are the two related? Here are the fat and sodium contents of several brands of burgers. a) Analyze the association between fat content and sodium using correla
